Question

Verify the commutative property for addition and multiplication for the rational numbers `(-10)/11` and `(-8)/33`

Answer 1

Let a = `(-10)/11` and b = `(-8)/33` be the given rational numbers.

Now a + b = `(-10)/11 + ((-8)/33)`

= `((-10 xx 3) + (-8 xx 1))/33`

= `(-30 + (-8))/33`

a + b = `(-38)/33`  ....(1)

b + a = `(-8)/33 + ((-10)/11)`

= `((-8 xx 1) + ((-10) xx 3))/33`

= `(-8 + (-30))/33`

b + a = `(-38)/33`   ....(2)

From (1) and (2)

a + b = b + a and hence addition is commutative for rational numbers

Further a × b = `(-10)/11 xx ((-8)/33) = 80/363`

a × b = `80/363` ....(3)

b × a = `(-8)/33 xx ((-10)/11) = 80/363`

b × a = `80/363`  ....(4)

From (3) and (4) a × b = b × a

Hence multiplication is commutative for rational numbers.